Method of producing gears



April 25, 1950 E. WILDHABER METHOD OF PRODUCING GEARS 2 Sheets-Sheet 1INVENTOR ERNEST W/LDHABER BY 2 At orney April 25, 1950 E. WILDHABERMETHOD OF PRODUCING GEARS Filed June 14, 1946 '2 Sheets-Sheet 2 R M WMm0 m w T 5 E N R F.

Patented Apr. 25, 1950 METHOD OF PRODUCING GEARS Ernest Wildhaber,Brighton, N. Y., assignor to Gleason Works, Rochester, N. Y., acorporation of New York Application June 14, 1946, Serial No. 676,678

15 Claims. 1

The present invention relates to longitudinally curved tooth gears andespecially to longitudinally curved tooth gears whose teeth are inclinedlengthwise to the straight line elements of the pitch surfaces of thegears. In particular the invention relates to tapered gears which havelongitudinally curved teeth and whoses axes are inclined to one another,at an angle of thirty degrees or less. The invention is applicable also,however, to gears which mesh with axes paral1el.

The standard method of generating bevel gears is to generate each memberof the pair conjugate to a crown gear whose axis intersects the axis ofthe blank in the cone apex of the blank. Where the gears, which are tobe out, have a small angle between their axes, this method of cuttinghas several disadvantages. In these gears, the cone distance, ordistance between the cone apex of the gear and a mean point in thecenter of its tooth face, is long in proportion to the width of thetooth face, and if each gear is generated conjugate to a crown gearwhose axis intersects the gear axis in the cone apex of the gear, a geargenerating machine is required of a size altogether out of proportion toth size of the gear to be cut. Moreover, such a gear generating machineis slow and costly to operate.

It is therefore the practice to generate angular bevel and hypoid gearsof long cone distance and small shaft angle on gear generating machineshaving a much smaller capacity as regards cone distance than the conedistance of the gears to be cut. This can be done by a process such asdescribed, for instance, in my Patent No. 2,310,484 of Feb. 9, 1943. Buteven with such methods as have been employed, heretofore, for cuttinglong cone distance tapered gears it has been difiicult to cut the gearson a machine of reasonable size with cutters or grinding Wheels ofpractical diameter. Moreover, with such methods, at least one member ofthe pair has to have its teeth out one side at a time. Furthermore,there are limitations as to the spiral angles which can be produced.

One object of the present invention is to provide a new tooth shape forlongitudinally curved tooth tapered gears which will permit of cuttingopposite sides of the tooth spaces of both membersof a pair of suchgears simultaneously.

A further object of the invention is to provide a new tooth shape forlongitudinally curved tooth gears which may be applied not only totapered gears of small cone angle, but to longitudinally curved toothgears which mesh with their axes at zero angle of inclination, that is,with their axes parellel, and which will permit of cutting oppositesides of the tooth spaces of such gears simultaneously.

Another object of the invention is to provide a method for cuttinglongitudinally curved tooth gears, which mesh with their axes inclinedat a small angle, which is free of limitation as to the spiral angleswhich may be cut, and with which spiral angles large enough for quietoperation at high speed may be provided.

A further object of the invention is to provide a method for cuttinglongitudinally curved tooth gears, which mesh with their axes inclinedat a small angle or at zero angle, on machines of a size proportionateto the size of the gears themselves.

Still another object of the invention is to provide a method for cuttinglongitudinally curved tooth gears, which mesh with their axes at a.slight angle or zero angle, in which a cutter or grinding wheel may beemployed of much smaller diameter than would ordinarily be used in thecutting of these gears, and which is of a size within the capacity andrange of a gear cutting or gear grinding machine that is of a sizeproportionate to the size of the gears.

Still another object of the invention is to provide a method for cuttinglongitudinally curved tooth gears, which mesh with axes at zeroinclination, that is, parallel, which may be practiced on a standardmachine for cutting spiral bevel or hypoid gears.

Other objects of the invention will be apparent hereinafter from thespecification and from the recital of the appended claims.

Gears produced according to the present invention have. teeth which areof greater thickness in the pitch plane at the ends of the teeth, wherethe spiral angle of the teeth is smaller, than at the ends where thespiral angle is greater. This is just the reverse of conventionalpractice. For longitudinally curved tooth tapered gears, this means thatthe teeth are thicker in the pitch plane at their inner ends thanattheir outer ends.

To compensate for this, longitudinally curved tooth gears made accordingto the present invention have teeth of greater depth at the end wherethe spiral angle is smaller than at the end of greater spiral angle.Again, this is just the reverse of conventional practice. Forlongitudinally curved toothed tapered gears, this means that the teetharedeeper at their inner ends than at their outer ends. balances thechange in tooth thickness.

This, however,

In generating bevel gears according to this invention both sides of atooth space are preferably cut simultaneously on both members of a gearpair; generation is effected about an axis off-set from the gear axisand not intersecting the gear axis in the gear apex as in conventiona1practice; the axis of generation is between the gear apex and the centerof curvature of its teeth; a varying ratio of roll is employed toproduce the desired tooth profile shapes; a cutter or grinding wheel ofrelatively small radius i employed; and this tool has cutting edgesprefer-'- ably of larger pressure angle than the pressure angle of thetooth surfacesto be produced so that the gear is rolled as though itwere'rolling with a surface outside its pitch surface on the pitchsurface of the crown gear or other basic gear represented by the tool.

In the drawings:

Figure 1 is a diagrammatic view illustrating the present invention, andmay be considered alsa's'ection taken through the pitch plane ofa'uasiecrcswn gear conjugate to a tapered gear produced according to oneembodiment of this invention, or as a development into its pitchpiafnefof'abevel gear produced according to one embodiment of thisinvention;

';Fig. 2*i's an axial sectional view of a bevel gear pair constructedaccording to the present invenues-and corresponding to the embodimentillustrated in Fig. 1;

Pig- 3 is a'diagrammatic view similar to Fig. 1

Turther illustrating the principles upon which the present inventionrests;

F gl isfa diagrammatic View illustrating the erieer of using a cutter orgrinding wheel of larger pressure angle than the gears themselves "theproduction of gears according to this 'if e h;

FigQiiis a diagrammatic view similar to Fig. 4 illustrating theapplication of the present injentitn tothe production of cylindricalgears, that is, gears which are to mesh with their axes rese r;

Fi 5 iSa diagrammatic view similar to Figs. 3 and-'5, illustrating amodified method of generating cylindrical gears according tothe presnfirivehtion; and

h1g7 is an axial sectional view of a cylindrical gear predated accordingto one embodiment of th s nvention.

In "Fig. '2, l0 and II denote, respectively, the two members of a pairof long cone distance bevel gears constructed according to the presentinvention. The axes l2 and I3, respectively, of these gears include anangle S with each other whichl'is'fs'maller than thirty degrees.

is 'the' common cone apex of these gears which is the point ofintersection of their axes. Theigears'have longitudinally curved teethwhich are inclined to the pitch line elements of the g s. Fi'g. '1 maybe considered as a develop- I'hen't mm the pitch plane of either one ofthe gears, "rasa section in the pitch plane of the basic crown 'gear towhich either gear is generated conjugate. As is shown, the gear haslongitudinally curved teeth 16 which are inclined to its'. pitch lineelement I1.

1'8 denotes a mean point in the pitch surface offthe gear shown indevelopment, and l8l9 is, the mean radius of curvature of the teeth N5of the gear, "the arc 20 indicating the mean ciiivature' circle of agear tooth. As is seen, the mean cone distance l5l8 of the gear is quitelarge as compared with the diameter of the gear,

and is also quite large as compared with the mean curvature radius l8-l9of its teeth.

Heretofore, it has been the practice to determine the center oflengthwise curvature of the teeth of tapered gears by projecting thecone apex of the gear to a normal to its tooth surface at a mean pointin the tooth length. Thus, according to prior practice, the curvatureradii for the teeth of longitudinally curved tooth tapered gears I0 andIl would be no less than the radius Iii-22, where 22 denotes the pointof projection of the cone apex it to the tooth nornial 23 at the meanpoint l8. With the present invention, a radius l8-l9- is selected forthe gear teeth which will permit using a cutter or grinding wheel whichis within the range of a gear cutting machine or gear grinding machineproportional in size to the gears being cut. Furthermore, with thepresent invention, the tooth spaces of the gears are made of uniformwidth from end to end measured at their roots so that opposite sides ofeach tooth space can be cut or ground simultaneously with a face millcutter orannular grinding wheel. With this construction, theteeth It ofthe gears are wider at their inner ends I, where the spiral angle orinclination of the teeth is smaller, than at their outer ends 0, wheretheir inclination or spiral angle is larger. In other words, the teethit of the gear's'hown in Fig. 1 are thicker at the smailer cone distancethan at the larger cone distance, their thickness increasing withdecreasing cone distance and with decreasing spiral angle.

To balance the variation in thickness of the teeth,jgears made accordingto the present invention have the further characteristic that the teethare deeper where they are thicker, that is, that their depth increasesfrom the outer to the inner ends of the teeth, namely, increases withthe decreasing spiral angle.

Preferably, the gears are generated substantially conjugateto basiccrown gears or basic members whose side tooth surfaces are surfaces ofrevolution, such as conical or spherical surfaces. Thus, the tooth side25 of the basic crown gear may be made'a convex spherical surface,centered at 25 and lying on a circle 26 below the pitch plane'Z'l (Fig.2) of the crown gear. Likewise, the tooth side 28 of the basic crowngear may be made a concave spherical surface centered at 28. The spherecenters of the various teeth of the crown gear all he on the circles 26and 2.9 which are centered on the axis 39 of thec'rowngear. This axispasses through cone apex IS. The sphere centers of several adjacenttooth sides are shown in Fig. 1, but only such-as-25' and 28, to whichspecific reference is made, have been designated by reference numerals.Mating tooth surfaces of the gears will be fully-matched when the basiccrown gears, to which the two gears in and H are generated conjugate,are exactly complementary.

Instead of having the teeth fully match one another, however, it ispreferable, as is'customary in spiral-bevel and hypoid gearing, to makethe teeth so that they have less than full length tooth hearing orcontact, the bearing being eased off toward the ends of the teeth. Thiscan be accomplished by using basic generating gears. and cutters orgrinding wheels which represent those gears, whose convex sphericalsurfaces are of larger radii than the radii of the concave sphericalsurfaces of those gears or tools. In any event, whether the toothsurfaces are fully matched or not, the two sides of a crown gear toothemployed for generating gears according to this invention can berepresented by a single face-mill cutter or annular grinding wheel whoseaxis passes through the two sphere centers of opposite sides of thecrown gear tooth. The opposite sides of the tooth space can besimultaneously generated in a rolling operation, for instance, in whichthe crown gear, which is represented by the tools, rolls and meshes withthe gear to be cut. When a tooth space has been cut, the tool iswithdrawn from engagement with the gear and the gear is indexed, andthen the next tooth space is produced, and so the operation continuesuntil the gear is completed.

The crown gear tooth represented by the single rotary cutter has, ofnecessity, a constant top land for the tip cutting edges of the cutterwill sweep out such a surface. By properly positioning the cutter withreference to the blank, however, gear teeth will be produced in theblank,

such as shown in Fig. 2, whose depth is greater at the inner ends I thanat the outer ends of the teeth. The gears, therefore, have teeth whosedepth changes from the outer to the inner end in correspondence with thechange in normal thickness of the teeth from end to end. The toothstrength is thereby well balanced along the whole length of the teethfrom their outer to their inner ends.

If we let A denote the mean cone distance I -I 8 of the gears, r thecurvature radius l8-I9, which is also the mean radius of the toolemployed in producing the gears, and s the mean spiral angle, that is,the inclination of a tangent 32 at mean point [8 to the pitch coneelement l1, then:

Distance l 5-22) =A.cos s Distance (Iii-22) =A.sin s The root lines 34and 35 of mating gears are preferably inclined at an angle cl to eachother which is such as to permit simultaneous generation of oppositesides of each tooth space on both members it and H of a gear pair.

It can be demonstrated mathematically that angle d, which corresponds tosuch simultaneous generation, may be computed as follows:

180 (A sin s I N,, tan p. cos 8 1* Here angle d, which is the sum of thededendum angles of the two gears, is given in degrees; 12 denotes thepressure angle of the gears, that is, the inclination of a normal to thetooth surface of the gear at mean point I8 to the pitch plane 21 of thecrown gear; and No is the number of teeth in the crown gear, which doesnot have to be an integral number. Ne equals the tooth number N ofeither gear divided by the sine of the pitch angle G of that gear, or:

N -ssc The circular pitch of the teeth of the gear is equal to 27A N cand this equals 21r( A. sin G) N ise ual to N. N

then the above formula can be transformed intoi Esin s sin G tan 10. coss N r N E i sin G) Ntanp. coss T Sns d N tan 12 1 In tapered gearsconstructed according to the present invention, then, it will be seenthat the teeth increase in depth from the outer to the inner ends of theteeth and that the teeth increase in width from the outer to the innerends of the teeth. Both features are contrary to standard practice intapered gears.

Where a gear is generated conjugate to a crown gear whose axis is at 36,a gear generator of quite large size must be employed. Such machines areheavy and slow. Moreover, they are expensive and a tooth cuttingoperation on these machines is costly.

Preferably, gears are generated by the present invention on relativelysmall size generators Which are faster and less expensive, and accordingto a preferred method of generation which will now be described. In thismethod, instead of rolling the gear and cutter relative to one anotherabout an axis 36 of a basic crown ear, whose axis intersects the axis ofthe blank in its cone apex, the rolling motion is produced about an axis49, which is parallel to axis 30 and which is located between the coneapex i5 of the gear and the center i9 of tooth curvature of the gear.This reduces the radial setting of the cutter to the distance 40-49 fromthe distance 55-49.

Each gear of the pair may then be generated by rotating the work on itsaxis and simultaneously effecting relative motion between the tool andthe work about the aXis 40 of the generating crown gear. In this motion,the cutter will swing relative to the work on a circle 4| concentric toaxis 40. The ratio of generating roll, that is, the ratio of rotation ofthe blank to the relative motion about axis 40, should be so modifiedthat, at infinitesimal distances away from point I9, the cutter axiswill have the positions 421 and 422, respectively, which lie on lines 43and 44, respectively, that pass through the points 42' and 42", thatdenote the opposite ends of the roll in conventional generation. Inother words, the angle [9-422 about aXis 40 corresponds to the turningangle I942" about axis I5, and likewise, the angle Iii-42; is equalsubstantially to the angle l9-42. The lines 43 and 44 are parallel tothe tangent 32 at mean point 18. The distance l9422 is greater than thedistance l9--421. Therefore, to generate proper tooth profiles on thegears l0 and II, when the axis of the generating gear is at 40, thecutter must be swung at a varying velocity about the axis of the crowngear or cradle during generation. This is in accordance with the basicprinciples set forth in my Patent No. 2,310,484 above mentioned. Bygenerating both members of the pair in thisway, gears l0 and l I will beproduced that are conjugate to each other.

Fig. 3 further illustrates the principle of generating gears accordingto the present invention with a rotary tool that is swung about axis 40.

l8'.. ;25' and -l8".Z8' denota respectively, the tooth normals at meanpoints l8 and l'8"in opposite sides of the spherical toothsurfaces of acrown gear tooth. In order to produce teeth which have full toothbearing or contact, the sphere radii for opposite sides of theteethshould be made equal and the sphere centers should be at 25 and 28',respectively. Actually, as already pointed out, less than full toothbearing is desirable, in order that the gears may accommodate themselvesto the variations in loads and in mounting that they encounter in use.Accordingly, a larger sphere radius is desired on the outside cuttingsurfaceand a smaller one on the inside cutting surface. The spherecenters are, therefore, preferably located at 25 and 28", respectively,away from points 25 and 28. Center 25 is displaced away from point 18along the tooth normal, While point 28" is displaced toward point 18"along the tooth normal.

' Points l8 and [8" are in generating contact with the tooth surfacebeing produced when they pas through the cone element ii, that is, whenthey are in position l8. Sphere center 25" is below point 25, so that,when point It lies on cone element ii, the connecting line with crowngear axis 40 of point 25" in its new position will appear in Fig. 3 as aline 45 which passes to the right of cone center i5. Sphere center 28 isin a raised position on account of the turning motion required to bringthe point l8 into coincidence with the point it. Hence, the line 45,which connects point 28" with center 48, when point l8 has been rotatedto position I8, passes to the left of cone center it. Points 8% and i3"have not been shown in the positions to which they are rotated ingeneration because the points would overlap other points shown andconfuse the illustration.

A proper tooth bearing without bias may be. obtained on the gear pairwhen the lines 55 and. 46 coincide with line l.5. i&.- To obtainthedesired bearing, when cutting both sidesv of. a tooth.. spacesimultaneously, the pressure. angle ofthe tool is increased. over thepressure angle .ofthe -gears themselves. In other words, a lowerpressure angle is generated on the gears than'is provided on the rotarytool employed in cutting or grinding them. This is illustrated in Fig.4where indicates fragmentarily ,a rotary .iace-mill or annular grindingwheel having opposite. sidecntting edges 5i and 52 whose pressureanglesare greater than the pressure angle oi the side surfaces 41 and 48 ofthe gear to be cut. The pressure angles of the sides 5i and 52 of theytool. are so selected that the points of contact 53 andj i between theoppositeside cuttingedges oi the tool and the opposite sides .of thetooth space being cut are generated in positions wherethe sphere centersand 28" of these sides lie on line. H5745. .56 and 5'1, respectively,are normals to the toothsides atthese points of contact and intersect atX. r

If a tool of the same pressure .angleas the gear teethwere to be used,such as is shown in broken lines at 5%, its oppositesidecntti edges. 5]"and,.52'., respectively, would contact ,the, sidesurfaces of the toothspace at 153 and.l.5 i,', .r espe.ctively. The normals 55', and.51',.respectively, at these points are inclined to the.norrnailslfifiand 51. Proper tooth bearing could not be obtained,therefore, if opposite sides of, a tooth space were to be outsimultaneouslywitha tool haginf ethe same pressure angle .as thepressureangle 'oithe tooth surfaces tobecut;

By phanging the generating pressure an le. the two mean points '18" "andl8""'o'f opposite tooth sides can be -gefneratedin any desired position.'They c'an be generated simultaneously if desired. in this caseItheinstantaneous axis of, generation would. have to fpass'lt'hro'ugh the.normals" at points 18 and I8 of the crown gear tooth. It would passthrough point l5 and through the intersection point of said normals withthat axial plane of the work which contains the work .axisi2 and theaxis 3!] of the basic crown gear. In this case, also, the spherelcenters25" and 28" would be in theshown positions when points It and 18" aregenerating the corresponding pointson the gears. Moreover, the lineswhich connect points 25 and 4B and points 28" and iii ,would taketheplace of lines 45 and 46. These connecting lines pass on opposite sidesof the cone center l5 from lines 45 and 46. The simultaneousgenerationof points 13 and I8", therefore, would produce more of achange than is required toproduce desired tooth bearing. The desiredbearing can beattained when the increase in generating pressure angle isjust enough ,for the points I8 and 1.8 to be generated on the work whentheir sphere centers 25" and 28" are on the line l5-4U.

vWherea tool, such .as the 1100159, is, used in generation of a gearaccording to the present invention, the gear is rolled, of course, withthe basic. crown gear represented by the tool as though a surface 58,larger thanthe .pitch surface as (Fig. 2) of the gear were .rolling .onthe pitch surface .16! of the basic crown gear.

If desired, ease-01f of the tooth profiles at top and the bottom can beobtained by properly shaping the" cutting edges of the .cutter orgrinding wheel. ThusQthe" axial profile of the outside cutting surfacernay be made less curved than the spherical profile, and the axialprofile'of the inside cutting'surface may be made more curved than thespherical profile, and this is done preferably onboth members. Profileease-off may also be obtained by modified generation.

Instead of using cutters 'orgrinding wheels which have curved cuttingedges, tools may be einployedrwhich have straight .cutting edges, thatis, tools may be eirrployed which have conical cutting surfaces. In allcases, the generation with tools, whosepres'sure angles are increasedover the pressure angles at which the gears run, afiords a convenientcontrolover the tooth shape and permits of avoidingbias bearing.

The combination .of .an increased generating pressureangle and anofi-set position between the work axis and the axis '40 of the generatedmember is applicable to drives .of any shaft anglesuch as a right angle.Itafioridslcontrol of the tooth bearing without resorting to a helicalgenerating motion providing that both members of the gear pair aregenerated.

An application of the principles of this invention to gears which are towhen parallel axes is illustrated in Figs. 5, 6, and 7. Here 10 denotesone member of apair of gears which are to run with their axes parallel.The axis of this gear is denoted at H and its pitch surface at 12, whichis a cylindrical surface coaxial of axis H.

The conventional and-natural basic member for generating such a gear isa rack instead of a crown gear. Fig. 5 shows the pitch plane section ofa basic rack- 15 havingteeth 16 which are curved longitudinally andwhose'spiral angle or helix angle increases from one end I of the teethto the other end '0. Thete'e'th have a larger thickness in the pitchplane ina direction normal to the teeth at the end I of smaller spiralangle than at the end of larger spiral angle. In accordance with thepresent invention, they are alsomade of greater depth at the end I thanat the end 0, the root lines 13 of the teeth being inclined to the pitchsurface 12 and to axis H of the gear and converging toward the end I ofthe teeth.

Preferably, the teeth of the basic rack are made with side surfaces thatextend along circular arcs. A mean lengthwise tooth spiral of the teethis a circular are such as shown at 11 in Fig. whose center is at 18. Thetooth sides 80 and 8! of the teeth of the basic rack may be madespherical surfaces. In the theoretical case of fully matched toothsurfaces, the radii of the convex spherical surfaces are equal to theradii of the concave spherical surfaces and the sphere centers 82 and 83of the sides 8! and 8|, respectively, are then projected into a singleline 85. The centers of curvature of several adjacent tooth sides havebeen shown on this line, but only centers 82 and 83 are designated bynumerals.

Preferably, the convex sides 88 of the rack teeth are made sphericalsurfaces of slightly larger radius than the concave sides 8| to generateteeth on the gears whose concave sides are less curved lengthwise thanthe convex sides of the teeth.

The tooth surfaces of the gear 10 are preferably cut two sidessimultaneously with a facemill cutter or annular grinding wheel byrotating the cutter or wheel in engagement with the blank whileeffecting a relative rolling motion between the tool and blank as thoughthe blank were rolling with the basic rack whose tooth is represented bythe tool. When one tooth space of the work has been cut or ground, thetool is withdrawn from engagement with the work and the work is indexed.Then the tool and work are reengaged and the next tooth space isgenerated. When the two members of a pair of gears are generatedconjugate to complementary basic racks in the manner described, thesetwo gears are fully conjugate to one another.

Fig. 6 illustrates a modified method of generating cylindrical gearsthrough which the gears may be cut or ground on a spiral bevel or hypoidgear generator. Instead of generating the tooth surfaces by rolling theWork with reference to the tool as though the work were rolling on abasic rack, the tool and work are rolled relative to one another aboutan axis 96 which is so positioned that the center 18 of the tool movesin the same direction as the basic rack would move in generation. Ingeneration, however, the tool bearing, a larger sphere radius is desiredon the outside cutting surface and a smaller one on the inside cuttingsurface. Thus, the sphere centers are displaced to points 88' and 89',from points 88 and 89, respectively. With this method, also, anincreased pressure angle is required on the tools to obtain the desiredshape of tooth bearing when both sides of a tooth space aresimultaneously generated. When increased pressure angle tools are used,the work is rolled, of course, with a surface of greater diameter thanits pitch surface on the surface of the gear or rack represented by thetool.

Since a grinding wheel is a cutter having an infinite number of cuttinedges, it will be understood that where the terms cutting and cutter areused in the claims, these terms are intended to cover grinding andgrinding wheels.

By the method of the present invention, then, it is possible to cutopposite sides of a tooth space of both members of a pair oflongitudinally curved tooth gears simultaneously, and byusing toolshaving cutting edges of greater pressure angle than the pressure angleof the tooth sides, which are to be produced, suitable square or ovaltooth bearings properly centered on the tooth sides can be obtained. Thepresent invention renders unnecessary, therefore, the employment of a.helical generating motion to accomplish this result. In this respect,the invention is applicable to drives of any shaft angle including gearswhose axes are at right angles to one another providing that bothmembers of the pair are generated.

While several different embodiments of the invention have beendescribed, then, it is to be understood that it is capable of furthermodification, and this application is intended to cover any variations,uses, or adaptations of the invention following, in general, theprinciples of the invention and including such departures from thepresent disclosure as come within known or customary practice in the artto which the invention pertains and as may be applied to the essentialfeatures hereinbefore set forth and as fall within the scope of theinvention or the limits of the appended claims.

Having thus described my invention, what I claim is:

1. The method of producing a cylindrical gear which comprises cuttingits teeth by moving a tool across the face of a gear b ank n a pathwhich has a varying inclination to straight line elements .of the pitchsurface of the gear, while effecting a relative rolling movement betweenthe tool and blank as though the gear being out were meshing with a gearrepresented by the tool, but varying the ratio of said rolling movementduring generation, the tool being so disposed relative to the blank asto cut tooth spaces in the blank of progressively greater depth from theend of the tooth which is of greater inclination to the pitch lineelements to the opposite end or the tooth.

2. The method of producing a gear which comprises cutting each of itsteeth by moving a tool across the face of a gear blank in a path whichhas a varying inclination to straight line elements of the pitch surfaceof the gear, while effectin a relative rolling motion between the toolandblank, the tool being so disposed to the blank as to cutprogressively deeper into the blank from the end of the tooth which isof greater inclination to the pitch line elements to the opposite end ofthe tooth.

3. The method of cutting a pair of longitudinally curved tooth gearswhich comprises cutting the tooth surfaces of each member of the pair bymoving a tool across the face of a gear blank in a path which has avarying inclination to straight line elements of the pitch surface ofthe gear, while effecting a relative rollingmovement between the tooland blank, the tool being so disposed to the blank as to cut teeth whichare progressively are or p egre'se tely' gleaterthick e's's end' wiiiehV deeperrromthe ends or the teeth which are or greatrinclination. to'thepitch line elements to the opposite ends of the .teeth.

The method of producing gearwhich coniprisescutting each ofits toothsurfaces by moving a tool across the face of a gear blank in a pathwhichhas a varying inclination to straight line elements r the pit chsurface of the ear, while efiecting a relative rolling movement at avarying ratio between thetool and blank, the toolbein so disposed to theblank as to cut progressively deeper into the tooth spacesof the blankfrom the end of the v eethwhic is or greater inclination to'the pitchline elements to the opposite d i h PQ tha v a of producing a gear whoseteeth have varying inclination along their'lengths to pitch lineelementsof the gear, which coniprises cutting opposite sides of itstootl'ispaces simultaneously by rotating a tool, whicli has oppositeside cutting edges whose pressure angle is greater than the pressureangl of the tooth,

surfaces to be cut, in engagement with the gear blank while producing arelative rolling' movement between the tool and blank at a varying ratioand as though the blank were rolling with a surface outside its pitchsurface on thepitch surface of a gear represente'd by the tool, the toolbeing so disposed relative to the blank as to cut tooth spaces in theblank which increase in depth from the end of thetooth, which is ofgreater inclination to the pitch line elements to the opposite end ofthe 'tooth.

6. The method of producing acyliridrical gear which comprises cuttingits teeth by moving a "tool across the face of a gear blank in a pathwhich has a varying inclination to straight line elements of thepitchsurface of the gear, while etfecting a relative rollingmovement betweenthe .tool and blank as though the gear were rolling with a basic rackrepresented by the tool, the

tool being so disposed relative to the blank as to out tooth spaces inthe blank which increase in depth frorn the end of the tooth' which isof greater inclination to the pitch line elements to the opposite end ofthe tooth,

'77. The method of producing a cylindrical gear *Which comprises cuttingits teeth by moving a tool across the faeeof agear blank in a path whichhas a varying inclination to straight line elements of thepitch suriaceof the gear, while efiecting a relative rolling motion between the tooland blank, the tool being sodisposed relative to the blank as to cuttooth spaces in'the blank of progressively greater depth from the end ofthe tooth which is of greater inclination to the pitch line elements tothe opposite end of the tooth. 7 i 4 a a v 8. The method of producing acylindrical gear whoseteeth have varying inclination to pitch lineelements of the gear along theirlengths, which comprises cuttingopposite sides of the tooth spaces simultaneously by rotating a tool,which has. opposite side cutting edges whose pressure e angle is greaterthan the pressure angle of the tooth surfaces to be cut, in engagementwith the gear blank .while producing a relative rolling movement betweenthe tool and blank as though the blank were rolling with a surfaceoutside its pitch surface on the pitch surface of a basic rackrepresented by the tool, but varyingthe 5 ratio of therollingmovfimentduring generation,

the tool being so disposed relative to the blank in depth fromthe end ofthe tooth which is of greater ineiinati'oh' to the pitch line elementsto the oppositeend of the tooth.

9. The method of producing a cylindrical gear which comprises cuttingits teeth by moving a tool across the fa c'e'of a gear blank in a pathwhich has'aV'ar'ying inclination to straight line elements of the pitchsurface of the blank, while effecting a relative rolling movement at avarying ratioibetween thetool and blank about an axis inclined to andoffset from the blank axis, the tool being so disposed to the blank asto cut tooth spaces in the blank increasing in depth from the ends ofthe teeth which are of greater inclination to the pitch line elements tothe opposite ends of the teeth. I

10. The method of producing a cylindrical gear whose teeth have varyinginclination to pitch line elements .of the gear along their lengths,which comprises cutting opposite sides of its tooth spacessimultaneously by rotating a tool, which has opposite side cutting edgeswhose pressure angle is greater than the pressure angle of theteetl'i tobe cut, in engagement with the gear blank while producing a relativerolling movement between the tool and blank at a varying ratio about anaxis inclined to and offset from the blank axis as though the blank wererolling with a surface outside its pitch surface on the pitch surface ofa gear represented by the tool, the toolbeing so disposed relative tothe blank asto cut tooth spaces in the blank which increase in depthfrom the ends of the teethwhich are of greater inclination to the pitchline ,elements' to the opposite ends of the teeth.

11. The method of producing a tapered gear which comprisescutting itsteeth by moving a tool across the" face of a gear blank in a path whichhas a varying inclination to straight line elements of the pitch surfaceof the blank, while effecting a relative rolling movement between thetool. and blank; the tool being so disposed relative to the blank as tocut tooth spaces in the blank which increase in depth from the outer tothe inner ends of the teeth. I

12. The method of producing a tapered gear which comprises cutting itsteeth by moving a tool across the face of a gear blank in a path whichhas a varying inclination to straight line elements of the pitch surfaceof the gear, while effecting a relative rolling movement between thetool and blank at a varying ratio, the tool being so disposed relativeto the blank as to cut tooth spaces in the blank which increase in depthfrom theouter to the inner ends of the teeth.

. 13; The method of producing a'tapered gear which comprises cutting twosides of its tooth spaces simultaneouslyby rotating a tool, which hasopposite side cutting edges whose pressure angle is greater than thepressure angle of the teeth to be cut, in engagement with the blankwhile producing a relative rolling movement be tween the tool and blankat a varying ratio about an axis angularly disposed to but offset fromthe axis of the blank and as thoughthe blank were rolling with a surfaceoutside its pitch surface on the pitch surface of a gear represented bythe tool, the tool being so disposed relative to the blank as to cuttooth spaces in the blank which increase in depth from the outer to theinner ends of the teeth. 14. The method of producing a pair of longi-.tudinally curved tooth gears, which comprises cutting opposite sides ofeach tooth space of each 13 member or the pair simultaneously byrotating a face-mill gear cutter, which has opposite side cutting edges,in engagement with a tapered gear blank while rotating the blank on itsaxis and simultaneously producing an additional relative motion betweenthe cutter and blank about an axis angularly disposed to the blank axisand offset from the blank axis and lying on a line which passes throughthe cutter axis and intersects the blank axis in the blank apex, theratio of the two last named movements being varied during generation. 1-

15. The method ofproduclng a pair of tapered gears, which comprisescutting opposite sides of each tooth space of. each member of the pairsimultaneously by moving a cutting tool, which has opposite side cuttingedges, in a longitudinally inclined path across the face of the blankwhile producing a relative rolling movement at a varying ratio betweenthe tool and blank about an axis angularly disposed to and oiiset fromthe blank axis.

ERNEST WILDHABER.

REFERENCES CITED The following references are of record in the file ofthis patent:

UNITED STATES PATENTS Number Name Date 1,404,504 Williams Jan. 24, 19221,588,560 Trbojerich June 15, 1926 1,848,342 Gleason Mar. 8, 19322,183,285 Wildhaber Dec. 12, 1939 2,310,484 Wildhaber Feb. 9, 1943

